Skip to main content

The Multiconfigurational (MC) SCF Method

  • Chapter
Methods in Computational Molecular Physics

Part of the book series: NATO ASI Series ((ASIC,volume 113))

Abstract

This series of lectures will treat the methods employed to solve the orbital and CI optimization problem for multiconfigurational wave functions. The main emphasis will be put on the recent development of quadratically or near-quadratically convergent procedures such as the Newton-Raphson and the super-CI methods. The equations for a general second order Newton-Raphson procedure will be derived in a form suitable for large scale applications. Different approximations to the general procedure will be discussed, such as the augmented Hessian and the super-CI methods.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Frenkel, J., “Wave Mechanics, Volume 2: Advanced General Theory” ( Clarendon, Oxford, 1934 ), pp. 460–462.

    Google Scholar 

  2. Hartree, D.R., Hartree, W. and Swirles, B., Phil.Trans.Roy.Soc. (London) A238, 229 (1939).

    ADS  Google Scholar 

  3. “Recent Developments and Applications of Multiconfiguration Hartree-Fock Methods” (NRCC Proceedings No. 10), Report LBL- 12151, Lawrence Berkeley Laboratory, University of California, Berkeley (1981).

    Google Scholar 

  4. Levy, B., Thesis CNRS No. A05271, Paris (1971); Levy, B., Int.J. Quantum Chem. 4, 297 (1970); Kendrick, J. and Hillier, I,. Chem. Phys. Letters 41, 283 (1976); Yeager, D.L. and Jürgensen, P., J. Chem. Phys. 71, 755 (1979); Roothaan, C.C.J., Detrich, J. and Hopper, D.G., Int.J. Quantum Chem. S13, 93 (1979); Werner, H.-J. and Meyer, W., J. Chem. Phys. 73, 2342 (1980); Lengsfield, B.H., J. Chem. Phys. 73, 382 (1980).

    Google Scholar 

  5. Levy, B., Thesis CNRS No. A05271, Paris (1971); Levy, B., Int.J. Quantum Chem. 4, 297 (1970); Kendrick, J. and Hillier, I,. Chem. Phys. Letters 41, 283 (1976); Yeager, D.L. and Jürgensen, P., J. Chem. Phys. 71, 755 (1979); Roothaan, C.C.J., Detrich, J. and Hopper, D.G., Int.J. Quantum Chem. S13, 93 (1979); Werner, H.-J. and Meyer, W., J. Chem. Phys. 73, 2342 (1980); Lengsfield, B.H., J. Chem. Phys. 73, 382 (1980).

    Article  Google Scholar 

  6. Levy, B., Thesis CNRS No. A05271, Paris (1971); Levy, B., Int.J. Quantum Chem. 4, 297 (1970); Kendrick, J. and Hillier, I,. Chem. Phys. Letters 41, 283 (1976); Yeager, D.L. and Jürgensen, P., J. Chem. Phys. 71, 755 (1979); Roothaan, C.C.J., Detrich, J. and Hopper, D.G., Int.J. Quantum Chem. S13, 93 (1979); Werner, H.-J. and Meyer, W., J. Chem. Phys. 73, 2342 (1980); Lengsfield, B.H., J. Chem. Phys. 73, 382 (1980).

    Article  ADS  Google Scholar 

  7. Levy, B., Thesis CNRS No. A05271, Paris (1971); Levy, B., Int.J. Quantum Chem. 4, 297 (1970); Kendrick, J. and Hillier, I,. Chem. Phys. Letters 41, 283 (1976); Yeager, D.L. and Jürgensen, P., J. Chem. Phys. 71, 755 (1979); Roothaan, C.C.J., Detrich, J. and Hopper, D.G., Int.J. Quantum Chem. S13, 93 (1979); Werner, H.-J. and Meyer, W., J. Chem. Phys. 73, 2342 (1980); Lengsfield, B.H., J. Chem. Phys. 73, 382 (1980).

    Article  ADS  Google Scholar 

  8. Levy, B., Thesis CNRS No. A05271, Paris (1971); Levy, B., Int.J. Quantum Chem. 4, 297 (1970); Kendrick, J. and Hillier, I,. Chem. Phys. Letters 41, 283 (1976); Yeager, D.L. and Jürgensen, P., J. Chem. Phys. 71, 755 (1979); Roothaan, C.C.J., Detrich, J. and Hopper, D.G., Int.J. Quantum Chem. S13, 93 (1979); Werner, H.-J. and Meyer, W., J. Chem. Phys. 73, 2342 (1980); Lengsfield, B.H., J. Chem. Phys. 73, 382 (1980).

    Google Scholar 

  9. Levy, B., Thesis CNRS No. A05271, Paris (1971); Levy, B., Int.J. Quantum Chem. 4, 297 (1970); Kendrick, J. and Hillier, I,. Chem. Phys. Letters 41, 283 (1976); Yeager, D.L. and Jürgensen, P., J. Chem. Phys. 71, 755 (1979); Roothaan, C.C.J., Detrich, J. and Hopper, D.G., Int.J. Quantum Chem. S13, 93 (1979); Werner, H.-J. and Meyer, W., J. Chem. Phys. 73, 2342 (1980); Lengsfield, B.H., J. Chem. Phys. 73, 382 (1980).

    Article  MathSciNet  ADS  Google Scholar 

  10. Levy, B., Thesis CNRS No. A05271, Paris (1971); Levy, B., Int.J. Quantum Chem. 4, 297 (1970); Kendrick, J. and Hillier, I,. Chem. Phys. Letters 41, 283 (1976); Yeager, D.L. and Jürgensen, P., J. Chem. Phys. 71, 755 (1979); Roothaan, C.C.J., Detrich, J. and Hopper, D.G., Int.J. Quantum Chem. S13, 93 (1979); Werner, H.-J. and Meyer, W., J. Chem. Phys. 73, 2342 (1980); Lengsfield, B.H., J. Chem. Phys. 73, 382 (1980).

    Article  ADS  Google Scholar 

  11. For a review of the second order optimization techniques see: Olsen, J. and Yeager, D.L., Adv. in Chem. Phys. (in press).

    Google Scholar 

  12. Roos, B., Chem. Phys. Letters 15, 153 (1972); Roos, B.O. and Siegbahn, P., in: “Methods of Electronic Structure Theory” (ed. H.F. Schaefer III ), Plenum Press (New York, 1977 ).

    Article  ADS  Google Scholar 

  13. Roos, B., Chem. Phys. Letters 15, 153 (1972); Roos, B.O. and Siegbahn, P., in: “Methods of Electronic Structure Theory” (ed. H.F. Schaefer III ), Plenum Press (New York, 1977 ).

    Google Scholar 

  14. Roos, B.O., Taylor, P.R. and Siegbahn, P.E.M., Chem. Phys. 48, 157 (1980); Siegbahn, P.E.M., Heiberg, A., Roos, B.O. and Levy, B., Phys. Scr. 21, 323 (1980); Siegbahn, P.E.M., Almlöf, J., Heiberg, A. and Roos, B., J. Chem. Phys. 74, 2384 (1981).

    Article  MathSciNet  Google Scholar 

  15. Roos, B.O., Taylor, P.R. and Siegbahn, P.E.M., Chem. Phys. 48, 157 (1980); Siegbahn, P.E.M., Heiberg, A., Roos, B.O. and Levy, B., Phys. Scr. 21, 323 (1980); Siegbahn, P.E.M., Almlöf, J., Heiberg, A. and Roos, B., J. Chem. Phys. 74, 2384 (1981).

    Article  ADS  Google Scholar 

  16. Roos, B.O., Taylor, P.R. and Siegbahn, P.E.M., Chem. Phys. 48, 157 (1980); Siegbahn, P.E.M., Heiberg, A., Roos, B.O. and Levy, B., Phys. Scr. 21, 323 (1980); Siegbahn, P.E.M., Almlöf, J., Heiberg, A. and Roos, B., J. Chem. Phys. 74, 2384 (1981).

    Article  ADS  Google Scholar 

  17. A recent MCSCF study of Cr2 yielded a wave function (for the \(^{1}\Sigma _{g}^{ + }\) ground state) comprising 3088 terms, where all CI coefficients were in the range -0.09 to +0.09: Bagus, P.S., Nelin C., Roos, B.O. and Siegbahn, P., to be published.

    Google Scholar 

  18. M. Moshinsky, “Group Theory and the Many-Body Problem” ( Gordon and Breach, New York, 1968 ).

    Google Scholar 

  19. Paldus, J. in: “Theoretical Chemistry: Advances and Perspectives” (eds. H. Eyring and D. Henderson), Vol. 2, ( Academic Press, New York, 1976 ) p. 131.

    Google Scholar 

  20. Shavitt, I., Int. J. Quantum Chem. S11, 131 (1977) and S12, 5 (1978).

    Google Scholar 

  21. Shavitt, I., Int. J. Quantum Chem. S11, 131 (1977) and S12, 5 (1978).

    Google Scholar 

  22. Wahl, A.C. and Das, G. in: “Methods of Electronic Structure Theory” (ed. H.F. Schaefer III ), Plenum Press (New York, 1977); Hinze, J., J. Chem. Phys. 59, 6424 (1973); Hinze, J., Int. J. Quantum Chem. S15, 69 (1981).

    Google Scholar 

  23. Wahl, A.C. and Das, G. in: “Methods of Electronic Structure Theory” (ed. H.F. Schaefer III ), Plenum Press (New York, 1977); Hinze, J., J. Chem. Phys. 59, 6424 (1973); Hinze, J., Int. J. Quantum Chem. S15, 69 (1981).

    Article  MathSciNet  ADS  Google Scholar 

  24. Wahl, A.C. and Das, G. in: “Methods of Electronic Structure Theory” (ed. H.F. Schaefer III ), Plenum Press (New York, 1977); Hinze, J., J. Chem. Phys. 59, 6424 (1973); Hinze, J., Int. J. Quantum Chem. S15, 69 (1981).

    Google Scholar 

  25. Levy, B. and Berthier, G., Int. J. Quantum Chem. 2, 307 (1968).

    Article  ADS  Google Scholar 

  26. Grein, F. and Chang, T.C., Chem. Phys. Letters 12, 44 (1977); Grein, F. and Banerjee, T.C., Int. J. Quantum Chem. S9, 147 (1975); J.Chem.Phys. 66, 1054 (1977); Cheung, L.M., Elbert, S.T. and Ruedenberg, K., Int.J. Quantum Chem. 14, 1069 (1979).

    Article  ADS  Google Scholar 

  27. Grein, F. and Chang, T.C., Chem. Phys. Letters 12, 44 (1977); Grein, F. and Banerjee, T.C., Int. J. Quantum Chem. S9, 147 (1975); J.Chem.Phys. 66, 1054 (1977); Cheung, L.M., Elbert, S.T. and Ruedenberg, K., Int.J. Quantum Chem. 14, 1069 (1979).

    Google Scholar 

  28. Grein, F. and Chang, T.C., Chem. Phys. Letters 12, 44 (1977); Grein, F. and Banerjee, T.C., Int. J. Quantum Chem. S9, 147 (1975); J.Chem.Phys. 66, 1054 (1977); Cheung, L.M., Elbert, S.T. and Ruedenberg, K., Int.J. Quantum Chem. 14, 1069 (1979).

    Google Scholar 

  29. Grein, F. and Chang, T.C., Chem. Phys. Letters 12, 44 (1977); Grein, F. and Banerjee, T.C., Int. J. Quantum Chem. S9, 147 (1975); J.Chem.Phys. 66, 1054 (1977); Cheung, L.M., Elbert, S.T. and Ruedenberg, K., Int.J. Quantum Chem. 14, 1069 (1979).

    Google Scholar 

  30. Lengsfield III, B.H., J. Chem. Phys. (in press); Lengsfield III, B.H. and Liu, B., J.Chem.Phys. 75, 478 (1981).

    Google Scholar 

  31. Lengsfield III, B.H., J. Chem. Phys. (in press); Lengsfield III, B.H. and Liu, B., J.Chem.Phys. 75, 478 (1981).

    Article  ADS  Google Scholar 

  32. Yaffe, L. and Goddard III, W.A., Phys.Rev. A13, 1682 (1976).

    ADS  Google Scholar 

  33. Dalgaard, E. and Jörgensen, P., J.Chem.Phys. 69, 3833 (1978).

    Article  ADS  Google Scholar 

  34. Olsen, J. and Yeager, D.L., preprint.

    Google Scholar 

  35. Pople, J.A., Krishnan, R., Schlegel, H.B. and Binkley, J.S., Int.J. Quantum Chem. S13, 225 (1979).

    Google Scholar 

  36. Yarkony, D.R., Chem.Phys. Letters 77, 634 (1981).

    Article  ADS  Google Scholar 

  37. MacDonald, J.K.L., Phys.Rev. 43, 830 (1933).

    Article  ADS  MATH  Google Scholar 

  38. AO integrals over symmetry orbitals are for example produced by the MOLECULE program system: J. Almlöf, Report 74-29 (December 1974), University of Stockholm, Institute of Physics, Stockholm, Sweden.

    Google Scholar 

  39. Roos, B., Int.J. Quantum Chem. S14, 175 (1980).

    Google Scholar 

  40. Shepard, R., Shavitt, I. and Simons, J., J.Chem.Phys. 76, 543 (1982).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1983 D. Reidel Publishing Company, Dordrecht, Holland

About this chapter

Cite this chapter

Roos, B.O. (1983). The Multiconfigurational (MC) SCF Method. In: Diercksen, G.H.F., Wilson, S. (eds) Methods in Computational Molecular Physics. NATO ASI Series, vol 113. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-7200-1_6

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-7200-1_6

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-009-7202-5

  • Online ISBN: 978-94-009-7200-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics